TSTP Solution File: SET916+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:01:59 EDT 2024
% Result : Theorem 3.87s 1.19s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 239 ( 79 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 307 ( 119 ~; 111 |; 69 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 2 sgn 89 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f11,conjecture,
! [X0,X1,X2] :
~ ( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
inference(negated_conjecture,[],[f11]) ).
fof(f14,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f17,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f26,f27]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK4(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK4(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f33]) ).
fof(f35,plain,
( ? [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X2),X1)
& ~ in(X2,X1)
& ~ in(X0,X1) )
=> ( ~ disjoint(unordered_pair(sK5,sK7),sK6)
& ~ in(sK7,sK6)
& ~ in(sK5,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
( ~ disjoint(unordered_pair(sK5,sK7),sK6)
& ~ in(sK7,sK6)
& ~ in(sK5,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f18,f35]) ).
fof(f40,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f28]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f28]) ).
fof(f56,plain,
! [X0,X1] :
( in(sK4(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
~ in(sK5,sK6),
inference(cnf_transformation,[],[f36]) ).
fof(f59,plain,
~ in(sK7,sK6),
inference(cnf_transformation,[],[f36]) ).
fof(f60,plain,
~ disjoint(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
! [X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f40]) ).
fof(f67,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f47]) ).
fof(f68,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f46]) ).
cnf(c_57,plain,
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_62,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f67]) ).
cnf(c_63,plain,
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_69,plain,
( in(sK4(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_70,negated_conjecture,
~ disjoint(unordered_pair(sK5,sK7),sK6),
inference(cnf_transformation,[],[f60]) ).
cnf(c_71,negated_conjecture,
~ in(sK7,sK6),
inference(cnf_transformation,[],[f59]) ).
cnf(c_72,negated_conjecture,
~ in(sK5,sK6),
inference(cnf_transformation,[],[f58]) ).
cnf(c_836,plain,
( in(sK4(X0,X1),X1)
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_62]) ).
cnf(c_837,plain,
( in(sK4(X0,X1),X0)
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_63]) ).
cnf(c_883,plain,
( sK4(unordered_pair(X0,X1),X2) = X0
| sK4(unordered_pair(X0,X1),X2) = X1
| disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_837,c_57]) ).
cnf(c_937,plain,
( in(sK4(X0,X1),X1)
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_62]) ).
cnf(c_938,plain,
( in(sK4(X0,X1),X0)
| disjoint(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_63]) ).
cnf(c_1053,plain,
( sK4(unordered_pair(X0,X1),X2) = X0
| sK4(unordered_pair(X0,X1),X2) = X1
| disjoint(unordered_pair(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_938,c_57]) ).
cnf(c_1180,plain,
( sK4(unordered_pair(sK5,sK7),sK6) = sK5
| sK4(unordered_pair(sK5,sK7),sK6) = sK7 ),
inference(superposition,[status(thm)],[c_883,c_70]) ).
cnf(c_1697,plain,
( sK4(unordered_pair(sK5,sK7),sK6) = sK5
| sK4(unordered_pair(sK5,sK7),sK6) = sK7 ),
inference(superposition,[status(thm)],[c_1053,c_70]) ).
cnf(c_2602,plain,
( sK4(unordered_pair(sK5,sK7),sK6) = sK5
| disjoint(unordered_pair(sK5,sK7),sK6)
| in(sK7,sK6) ),
inference(superposition,[status(thm)],[c_1180,c_836]) ).
cnf(c_4756,plain,
sK4(unordered_pair(sK5,sK7),sK6) = sK5,
inference(global_subsumption_just,[status(thm)],[c_1697,c_71,c_70,c_2602]) ).
cnf(c_4765,plain,
( disjoint(unordered_pair(sK5,sK7),sK6)
| in(sK5,sK6) ),
inference(superposition,[status(thm)],[c_4756,c_937]) ).
cnf(c_4768,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4765,c_70,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 21:00:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.87/1.19 % SZS status Started for theBenchmark.p
% 3.87/1.19 % SZS status Theorem for theBenchmark.p
% 3.87/1.19
% 3.87/1.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.87/1.19
% 3.87/1.19 ------ iProver source info
% 3.87/1.19
% 3.87/1.19 git: date: 2024-05-02 19:28:25 +0000
% 3.87/1.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.87/1.19 git: non_committed_changes: false
% 3.87/1.19
% 3.87/1.19 ------ Parsing...
% 3.87/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.87/1.19
% 3.87/1.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.87/1.19
% 3.87/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.87/1.19
% 3.87/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.87/1.19 ------ Proving...
% 3.87/1.19 ------ Problem Properties
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 clauses 23
% 3.87/1.19 conjectures 3
% 3.87/1.19 EPR 5
% 3.87/1.19 Horn 18
% 3.87/1.19 unary 9
% 3.87/1.19 binary 6
% 3.87/1.19 lits 47
% 3.87/1.19 lits eq 16
% 3.87/1.19 fd_pure 0
% 3.87/1.19 fd_pseudo 0
% 3.87/1.19 fd_cond 0
% 3.87/1.19 fd_pseudo_cond 6
% 3.87/1.19 AC symbols 0
% 3.87/1.19
% 3.87/1.19 ------ Input Options Time Limit: Unbounded
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 ------
% 3.87/1.19 Current options:
% 3.87/1.19 ------
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 ------ Proving...
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 ------ Proving...
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 ------ Proving...
% 3.87/1.19
% 3.87/1.19
% 3.87/1.19 % SZS status Theorem for theBenchmark.p
% 3.87/1.19
% 3.87/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/1.19
% 3.87/1.20
%------------------------------------------------------------------------------